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**R.2 Integer Exponents, Scientific Notation, and Order of Operations**

Simplify expressions with integer exponents. Solve problems using scientific notation. Use the rules for order of operations. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

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**Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley**

Integers as Exponents When a positive integer is used as an exponent, it indicates the number of times a factor appears in a product. For any positive integer n, where a is the base and n is the exponent. Example: 84 = 8 • 8 • 8 • 8 For any nonzero real number a and any integer m, a0 = 1 and Example: a) 80 = b) Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

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**Properties of Exponents**

Product rule Quotient rule Power rule (am)n = amn Raising a product to a power (ab)m = ambm Raising a quotient to a power Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

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**Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley**

Examples – Simplify. a) r 2 • r 5 = r (2 + 5) = r 3 b) c) (p6)4 = p ‒24 or d) (3a3)4 = 34(a3)4 = 81a12 or e) Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

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**Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley**

Scientific Notation Use scientific notation to name very large and very small positive numbers and to perform computations. Scientific notation for a number is an expression of the type N 10m, where 1 N < 10, N is in decimal notation, and m is an integer. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

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**Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley**

Examples Convert to scientific notation. a) 17,432,000 = 107 b) = 2.4 1010 Convert to decimal notation. a) 106 = 3,481,000 b) 105 = Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

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**Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley**

Another Example Chesapeake Bay Bridge-Tunnel. The 17.6-mile-long tunnel was completed in Construction costs were $210 million. Find the average cost per mile. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

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**Rules for Order of Operations**

Do all calculations within grouping symbols before operations outside. When nested grouping symbols are present, work from the inside out. Evaluate all exponential expressions. Do all multiplications and divisions in order from left to right. Do all additions and subtractions in order from left to right. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

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**Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley**

Examples a) 4(9 6)3 18 = 4(3)3 18 = 4(27) 18 = 108 18 = 90 b) Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

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